This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.
A framework for financial market modeling, the benchmark approach extends beyond standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. This book presents the necessary mathematical tools, followed by a thorough introduction to financial modeling under the benchmark approach, explaining various quantitative methods for the fair pricing and hedging of derivatives.
This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.
Financial modelling Theory, Implementation and Practice with MATLAB Source Jörg Kienitz and Daniel Wetterau Financial Modelling - Theory, Implementation and Practice with MATLAB Source is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk-neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.
The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
In Volatility Trading, Sinclair offers you a quantitative model for measuring volatility in order to gain an edge in your everyday option trading endeavors. With an accessible, straightforward approach. He guides traders through the basics of option pricing, volatility measurement, hedging, money management, and trade evaluation. In addition, Sinclair explains the often-overlooked psychological aspects of trading, revealing both how behavioral psychology can create market conditions traders can take advantage of-and how it can lead them astray. Psychological biases, he asserts, are probably the drivers behind most sources of edge available to a volatility trader. Your goal, Sinclair explains, must be clearly defined and easily expressed-if you cannot explain it in one sentence, you probably aren't completely clear about what it is. The same applies to your statistical edge. If you do not know exactly what your edge is, you shouldn't trade. He shows how, in addition to the numerical evaluation of a potential trade, you should be able to identify and evaluate the reason why implied volatility is priced where it is, that is, why an edge exists. This means it is also necessary to be on top of recent news stories, sector trends, and behavioral psychology. Finally, Sinclair underscores why trades need to be sized correctly, which means that each trade is evaluated according to its projected return and risk in the overall context of your goals. As the author concludes, while we also need to pay attention to seemingly mundane things like having good execution software, a comfortable office, and getting enough sleep, it is knowledge that is the ultimate source of edge. So, all else being equal, the trader with the greater knowledge will be the more successful. This book, and its companion CD-ROM, will provide that knowledge. The CD-ROM includes spreadsheets designed to help you forecast volatility and evaluate trades together with simulation engines.
